      # Solids Of Revolution

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### #1 TZ250

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Posted 04 February 2010 - 03:28 PM

In class we're working on solids of revolution. How do I make the CP330 draw something like that? I can rotate a 3D function, and shade the difference between two functions, but I don't know how to revolve a function.

Example: The region bounded by y=(square root of X) , y=2X+1, X=1 and X=4.

How do I draw that? (in solid form)

### #2 ASTRO491K

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Posted 06 February 2010 - 02:06 AM

Keep in mind that unlike shading the difference between two functions in the x-y plane, solids of revolution are just that, solids. That requires that you plot the 3d surface equivalent of the solid of revolution, for example rotataing the semi-circle y=sqrt(1-x^2) about the x axis is equivalent to plotting the 3d surface x^2+y^2+z^2=1, i.e., z=+/-sqrt(1-x^2-y^2). I hope this reply is helpful because to my knowledge there is no built in function for displaying the rotated solid of revolution. Of course I could be wrong.

In class we're working on solids of revolution. How do I make the CP330 draw something like that? I can rotate a 3D function, and shade the difference between two functions, but I don't know how to revolve a function.

Example: The region bounded by y=(square root of X) , y=2X+1, X=1 and X=4.

How do I draw that? (in solid form)

### #3 Kilburn

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Posted 06 February 2010 - 09:24 PM

Is this what you need? In the 3D Graph app, press the "Z=" button so it turns into "Xst", that will allow you to graph 3D parametric equations. If you want to rotate a function around an axis and see what it looks like, here's the formula:

X(s,t) = cos(t) * f(s)
Y(s,t) = sin(t) * f(s)
Z(s,t) = s

Where f is the function you want to revolve. Just look at the above picture, I did that with the square root function. Just modify smin and smax in the axis properties if you want a wider range.

### #4 ASTRO491K

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Posted 07 February 2010 - 03:39 AM

Wow, that is really nice Kilburn. Could you then plot an additional surface, say the plane z=1-x-y to show how it intersects with the paraboloid that you already have? That would be really really super!

Is this what you need? In the 3D Graph app, press the "Z=" button so it turns into "Xst", that will allow you to graph 3D parametric equations. If you want to rotate a function around an axis and see what it looks like, here's the formula:

X(s,t) = cos(t) * f(s)
Y(s,t) = sin(t) * f(s)
Z(s,t) = s

Where f is the function you want to revolve. Just look at the above picture, I did that with the square root function. Just modify smin and smax in the axis properties if you want a wider range.

### #5 Kilburn

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Posted 07 February 2010 - 08:11 PM

Wow, that is really nice Kilburn. Could you then plot an additional surface, say the plane z=1-x-y to show how it intersects with the paraboloid that you already have? That would be really really super!

Nope, as far as I know, you can't even draw several surfaces at once. ### #6 ASTRO491K

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Posted 07 February 2010 - 11:38 PM

Nope, as far as I know, you can't even draw several surfaces at once. Hi Kilburn, me again. Isn't there some way to generate and store a surface, and then generate the second surface and store it, and then simply display both? If that was possible, it would be totally awesome!

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